Why Exponents Don't Always Add Up

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Homework Help Overview

The discussion revolves around the properties of exponents, specifically focusing on the behavior of negative and positive bases when multiplied. The original poster questions why certain exponent rules seem to apply differently in two scenarios involving the base of -1 and 1.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the rules of exponents, questioning the conditions under which they apply, particularly regarding the necessity of having the same bases for exponent addition.

Discussion Status

Some participants have offered insights into the properties of exponents, noting that the base must be the same for the addition of exponents to hold true. The conversation appears to be ongoing, with participants reflecting on their understanding and clarifying concepts.

Contextual Notes

The original poster expresses confusion about the application of exponent rules, indicating a potential misunderstanding of the foundational principles involved. There is also an acknowledgment of common mistakes in reasoning about exponents.

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Homework Statement



Why is ##(-1)^{n+1} (-1)^{n+1} = (-1)^{2n+2}## but
##(-1)^{n+1} (1)^{n+1} = (-1)^{n+1}##
I thought in both instances you are to just add the exponents.



Homework Equations





The Attempt at a Solution


 
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1 to the power of anything is just 1. Right?

EDIT : Also, to be a bit more general, you need to have the same bases.
 
Thanks. I can't even believe myself some days
 
Jbreezy said:
Thanks. I can't even believe myself some days

Ha no problem :), we all have those.
 
Because:
I:
[tex]a^x\cdot a^x=a^{x+x}[/tex]
II:
[tex]a^x\cdot b^x=(a\cdot b)^{x}[/tex]
 

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